Tuning spin-density separation via finite-range interactions: Dimensionality-driven signatures in dynamic structure factors

TL;DR

This paper explores how finite-range interactions influence spin-density separation in two-component bosonic gases, revealing that dimensionality dramatically affects excitation spectra and collective behaviors, with implications for ultracold atom experiments.

Contribution

It provides an analytical framework for understanding finite-range interaction effects on spin-density separation across different dimensions, extending beyond contact interactions.

Findings

In 1D, spin and density peaks shift to higher frequencies with stronger interactions.

In 3D, peaks shift to lower frequencies and become broader.

Dimensionality critically influences collective excitation responses.

Abstract

Spin-density (charge) separation, marked by distinct propagation velocities of spin and density excitations, epitomizes strong correlations, historically confined to one-dimensional (1D) systems. The recent experimental work of S. Dhar, B. Wang, M. Horvath, et al. Nature 642, 53 (2025), using a weakly interacting 3D Bose-Einstein condensate of $^{133}$Cs atoms confined in a 2D optical lattice to realize spin-density separation and demonstrate boson anyonization, motivates a deeper exploration into how dimensionality and interactions govern quantum correlations. In this work, we investigate this in two-component bosonic mixtures with finite-range interactions, probing 1D and 3D dynamics. Using path integral effective field theory within the one-loop approximation, we derive analytical expressions for zero-temperature ground-state energy and quantum depletion, seamlessly recovering contact interaction results in the contact limit. By crafting an effective action for decoupled density and spin modes, we compute dynamic structure factors (DSFs), revealing how finite-range interactions sculpt spin-density separation. A pivotal finding is the dimensionality-driven divergence in DSF peak dynamics: in 1D, peaks ascend to higher frequencies with increasing interaction strength, yielding sharp responses; in 3D, peaks descend to lower frequencies, with broader density wave profiles. These insights highlight dimensionality's critical role in collective excitations and provide a robust theoretical blueprint for probing interaction-driven quantum phenomena via Bragg spectroscopy, paving new pathways for exploring dimensionally tuned quantum correlations in ultracold quantum gases.